Problem: Multiply the following complex numbers: $({4}) \cdot ({-2-2i})$
Answer: Complex numbers are multiplied like any two binomials. First use the distributive property: $ ({4}) \cdot ({-2-2i}) = $ $ ({4} \cdot {-2}) + ({4} \cdot {-2}i) + ({0}i \cdot {-2}) + ({0}i \cdot {-2}i) $ Then simplify the terms: $ (-8) + (-8i) + (0i) + (0 \cdot i^2) $ Imaginary unit multiples can be grouped together. $ -8 + (-8 + 0)i + 0i^2 $ After we plug in $i^2 = -1$ , the result becomes $ -8 + (-8 + 0)i - 0 $ The result is simplified: $ (-8 - 0) + (-8i) = -8-8i $